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Table 2 Processing times of System 1

From: A higher-order numerical framework for stochastic simulation of chemical reaction systems

    τ   
  0.05 0.1 0.2 0.4 0.8
ETL 21.3 (9.2) 13.3 (18.4) 7.63 (37.1) 4.08 (74.7) 2.21 (152.0)
xETL - 34.3 (0.05) 21 (0.16) 11.8 (0.61) 6.34 (2.6)
xxETL - - (-MC) 42.1 (0.015) (-MC) 25 (0.016) 14 (0.043)
MPTL 21.3 (0.024) 13.4 (0.070) 7.65 (0.25) 4.18 (1.0) 2.24 (4.2)
xMPTL - (-MC) 34.7 (0.0088) (-MC) 21.1 (0.0082) (-MC) 11.8 (0.0026) 6.38 (0.041)
xxMPTL - - (-MC) 42.4 (0.0089) (-MC) 25.2 (0.0090) (-MC) 14 (0.0088)
TTTL 40.8 (0.017) 21.1 (0.063) 13.3 (0.26) 7.65 (1.1) 4.17 (4.2)
xTTTL - (-MC) 62.1 (0.0016) (-MC) 34.6 (0.0022) (-MC) 20.9 (0.0044) 11.8 (0.041)
xxTTTL - - (-MC) 75.4 (0.0022) (-MC) 42.2 (0.0031) (-MC) 25.1 (0.011)
  1. Processing times (in thousands of seconds) of 108 simulations of System 1 using Euler τ-leap, midpoint τ-leap and θ-trapezoidal τ-leap methods and their extrapolated and double-extrapolated versions. Absolute errors in the mean from the analytical values are included in brackets. For comparison, implementation of 108 simulations of an SSA using the Direct Method would take approximately 1.2 × 105seconds. Entries marked (-MC) are thought to be below the Monte Carlo error level; bold entries are faster than the un/single-extrapolated versions with similar error level (i.e. compare with one row above).